Complete the square to solve for $x$. $4x^{2}+4x+1 = 0$
First, divide the polynomial by $4$ , the coefficient of the $x^2$ term. $x^2 +x + \dfrac{1}{4} = 0$ Note that the left side of the equation is already a perfect square trinomial. The coefficient of our $x$ term is $1$ , half of it is $\dfrac{1}{2}$ , and squaring it gives us ${\dfrac{1}{4}}$ , our constant term. Thus, we can rewrite the left side of the equation as a squared term. $( x + \dfrac{1}{2} )^2 = 0$ Take the square root of both sides. $x + \dfrac{1}{2} = 0$ Isolate $x$ to find the solution(s). The solution is: $x = -\dfrac{1}{2}$ We already found the completed square: $( x + \dfrac{1}{2} )^2 = 0$